I made an algorythm that uses the probability distribution. And while technically O(n), it is simply always slower than quick sort. That is because at low amounts of n it simply has a bigger constant multiplier and at higher n's it has the same issue as counting sort since it can't use the cache like quick sort, so each memory access becomes slower the higher a cache level it uses. That and the fact that it realistically never gets better than O(nlog(log(n))) is why it is simply not good.